The generator matrix

1 0 0 0 0 0 1 1 1 2 1 1 2 1 1 0 1 1 1 1 2 0 1 0 1 2 2 0 1 1 0 2 1 1 2 0 1 0 1 0 0 1 1 2 0 1 1 1 0 2 1 1 1 1 1 1 2 1 0 1 1 2 2 1 2 2 1 0 2 1 1 1 1 0 1 1 2 1 1 0 1
0 1 0 0 0 0 0 0 0 0 0 2 2 1 1 1 3 1 1 3 0 1 3 1 0 2 1 1 3 2 1 2 0 1 1 2 2 1 3 1 1 0 0 1 2 1 3 0 1 1 2 3 3 0 2 1 0 3 0 1 2 0 2 1 1 2 2 2 0 2 0 1 1 1 2 3 0 0 0 1 0
0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 3 3 2 2 1 1 0 2 1 3 1 3 2 1 1 3 1 2 1 0 2 0 2 0 2 1 1 0 1 1 2 0 3 2 1 0 3 3 2 3 1 2 2 1 1 0 2 1 3 0 0 3 2 1 2 2 0 3 1 1 0 2 1 3 1 0
0 0 0 1 0 0 0 1 1 1 2 1 3 3 2 3 1 2 0 3 0 2 1 1 2 1 2 3 0 3 0 1 3 3 2 1 2 2 3 1 2 3 1 0 1 2 1 3 1 2 0 1 1 0 0 0 2 1 1 1 0 1 3 3 3 1 2 2 3 1 2 1 0 3 3 1 1 0 1 1 0
0 0 0 0 1 0 1 0 1 3 2 1 3 3 3 0 2 0 1 3 1 1 2 3 3 2 3 0 0 0 2 0 1 0 1 0 3 2 2 3 0 2 2 2 2 0 0 3 1 3 0 3 1 0 3 2 0 1 3 1 0 1 0 0 1 2 3 1 1 3 3 0 1 3 3 1 1 2 2 0 0
0 0 0 0 0 1 1 3 2 1 1 1 0 1 3 2 1 1 2 2 3 3 0 3 0 1 2 1 0 2 3 1 0 3 3 0 3 0 0 0 2 1 0 0 0 2 3 0 1 1 1 3 1 2 1 3 1 3 2 2 1 0 3 2 2 0 0 1 1 2 2 2 0 0 3 2 2 0 0 2 0
0 0 0 0 0 0 2 2 0 2 2 2 0 2 2 0 2 2 0 0 2 2 0 2 0 2 0 2 2 2 0 0 2 0 0 2 0 2 2 2 2 0 2 0 2 0 0 2 0 2 0 2 0 2 0 2 2 0 2 2 2 0 2 2 0 2 2 0 0 0 0 2 2 2 0 0 0 2 0 2 0

generates a code of length 81 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+51x^68+50x^69+161x^70+226x^71+295x^72+352x^73+300x^74+404x^75+427x^76+422x^77+406x^78+402x^79+454x^80+430x^81+457x^82+458x^83+360x^84+432x^85+382x^86+324x^87+296x^88+262x^89+245x^90+174x^91+120x^92+80x^93+82x^94+48x^95+38x^96+20x^97+10x^98+12x^99+6x^100+4x^102+1x^110

The gray image is a code over GF(2) with n=162, k=13 and d=68.
This code was found by Heurico 1.10 in 4.79 seconds.